Interlayer Breathing and Shear Modes in Few-Trilayer MoS2 andWSe2Yanyuan Zhao,† Xin Luo,‡ Hai Li,§ Jun Zhang,† Paulo T. Araujo,∥ Chee Kwan Gan,‡ Jumiati Wu,§

Hua Zhang,*,§ Su Ying Quek,*,‡ Mildred S. Dresselhaus,∥,⊥ and Qihua Xiong*,†,#

†Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21Nanyang Link, Singapore 637371‡Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632§School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798∥Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts02139, United States⊥Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States#Division of Microelectronics, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798

*S Supporting Information

ABSTRACT: Two-dimensional (2D) layered transition metaldichalcogenides (TMDs) have recently attracted tremendousinterest as potential valleytronic and nanoelectronic materials,in addition to being well-known as excellent lubricants in thebulk. The interlayer van der Waals (vdW) coupling and low-frequency phonon modes and how they evolve with thenumber of layers are important for both the mechanical andthe electrical properties of 2D TMDs. Here we uncover theultralow frequency interlayer breathing and shear modes infew-layer MoS2 and WSe2, prototypical layered TMDs, usingboth Raman spectroscopy and first principles calculations.Remarkably, the frequencies of these modes can be perfectlydescribed using a simple linear chain model with only nearest-neighbor interactions. We show that the derived in-plane (shear) and out-of-plane (breathing) force constants from experimentremain the same from two-layer 2D crystals to the bulk materials, suggesting that the nanoscale interlayer frictional characteristicsof these excellent lubricants should be independent of the number of layers.

KEYWORDS: Transition metal dichalcogenides, shear modes, breathing modes, Raman spectroscopy, first principle calculations,linear chain model

Bulk transition metal dichalcogenides (TMDs) represent afamily of about 40 layered compounds, with wide-ranging

electronic properties and excellent mechanical properties aslubricants due to their weak interlayer interactions.1 Few-layer2D TMD crystals, motivated by the experimental isolation2 andrecent scaled-up synthesis,3−5 have been shown to have uniqueelectronic and optical properties. For instance, the bandgap of2D MoS2 crystals exhibits an indirect-to-direct transition from afew-layer to monolayer sample,6 while monolayer MoS2 andseveral related TMDs have been proposed as possiblevalleytronics materials7−11 and were demonstrated as field-effect transistors.12,13 Recent calculations predict that the carriermobility in a MoS2 monolayer is limited by optical phononscattering due to deformation potential and Frohlichinteractions.14 Similarly, we expect low-frequency interlayerphonons to especially affect the low bias electron transportbehavior via electron−phonon coupling interactions. Thepossible application of 2D TMDs as components in nanoscale

electromechanical systems implies that a systematic under-standing of their mechanical properties is required. Recently,frictional characteristics of 2D TMDs, as measured usingatomic force microscopy (AFM), were found to be highlydependent on the number of layers.15 However, the AFMmeasured friction between the tip and the entire 2D crystal,involving a negligible interlayer sliding.15 The interlayerinteractions are dominated by weak van der Waals interactionsthat are inherently nonlocal. It is thus an open and importantquestion to understand how the interlayer interactions evolvefrom 3D bulk to 2D TMDs, thus elucidating the interlayersliding contributions in friction. Therefore, probing lowfrequency interlayer phonon modes and interlayer force

Received: November 11, 2012Revised: February 24, 2013Published: February 24, 2013

Letter

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constants in 2D TMD crystals and their evolution as a functionof the number of layers have become increasingly important.Raman spectroscopy has been very successful in studying

phonons and their couplings to electrons in 2D crystals likegraphene in the few-layer regime.16 The probing of theinterlayer phonons through Raman spectroscopy is challenging,since these phonon modes are usually of very low frequencies(several to tens of wavenumbers) and are difficult to bedistinguished from the Rayleigh background scattering. Thelow-frequency characteristic of the interlayer phonon modesresults from the weak interlayer vdW restoring force. By using atriple-grating micro Raman spectrometer and effective filters(see Methods), we can detect frequencies as low as ∼5 cm−1,providing a unique capability of probing low energy phononmodes. In this work, we uncover, using a combination ofRaman spectroscopy and first principles calculations, theexistence of two shear modes and two breathing modes in theultralow frequency (<55 cm−1) region for few-layer MoS2 andWSe2. Similar interlayer shear modes have been identified byRaman spectra in a series of bulk layered materials such asgraphite,17 h-BN,18 NbSe2,

19 GaS,20 MoS2,21 and WSe2,

22 andrecently in both few-layer graphene23 and MoS2 crystals.

24 The“organ pipe” or “breathing” modes as reported here cannot beoptically probed in bulk layered materials because of theiroptical inactivity, but they might become IR or Raman active astheoretically predicted by Michel and Verberck in multilayergraphene and BN.25 Although a few experimental works onfew-layer graphene have reported the overtones of theinterlayer breathing modes (ZO, ZA) and other high-frequencyphonon modes (LO, oTO) through combination mode Ramanscattering,26,27 so far, the interlayer breathing modes have notyet been directly probed by any optical techniques in the low-frequency region. Here, we find that the frequencies of theexperimentally observed shear modes in few-layer MoS2 andWSe2 redshift as the number of layers decreases, while theobserved breathing modes evolve with an opposite trend. Thesefrequencies can be perfectly described using a simple linearchain model with only nearest-neighbor interactions, with eachconstituent of the chain representing one layer. Using thismodel, we can extract both the in-plane (shear) and out-of-plane (breathing) force constants from experiment. Remark-ably, these force constants remain the same from two-layer 2Dcrystals to the bulk materials, suggesting that the nanoscaleinterlayer frictional characteristics of these excellent lubricantsshould be independent of the number of layers.Layered TMDs, that is, MX2 (M = transition metal, X = S,

Se, Te), are composed of hexagonal close-packed atomic layers.Each layer, henceforth referred to as “trilayer (TL)”, consists ofthree atomic layers, covalently bonded to one another, and theadjacent TLs are coupled via weak vdW interactions. The MX2compounds investigated here are of the most common 2H type(atomic layers arranged in /AbA BaB/ stacking, as shown inFigure 2a), which belongs to the non-symmorphic space groupD6h

4 (P63/mmc).1 The primitive unit cell consists of two TLs(six atoms), resulting in 18 Brillouin zone center (Γ) phonons.The irreducible representations of the phonon modes areshown as Γbulk = A1g + 2A2u + B1u + 2B2g + E1g + 2E1u + E2u +2E2g, among which 2E2g, E1g, and A1g are Raman active modes.The 2-fold degenerate E symmetry modes represent in-plane(shear) vibrations, while the A modes vibrate in the out-of-plane (breathing) direction along the z-axis. In the few-TLsamples prepared by mechanical exfoliation, we believe the/AbA BaB/stacking order is maintained. The symmetry along

the z-axis is reduced in few-TL crystals due to the lack oftranslation in its direction, and therefore the symmetryoperations are reduced from 24 in the bulk to 12 in even-and odd-TLs each, with symmetry groups different from thatfor the bulk 2H materials (D6h

4 ). The symmetry operations infew-TLs are demonstrated in Figure 1, using 1TL and 2TL as

examples for odd- and even-TLs, respectively. The 12symmetry operations in odd-TLs are: E (identity symmetry),2C3 (the axis of the clockwise and anticlockwise rotations isshown in Figure 1a), 3C2′ (the three rotation axes are shown inFigure 1b and are lying in the σh plane), σh (the horizontalreflection plane is represented as the gray plane in Figure 1a),2S3 (two C3 rotations followed by a σh reflection), 3σv (one ofthe vertical reflection planes is represented as the yellow planein Figure 1a, and the top views are shown as the green solidlines in Figure 1b). Similarly, the 12 symmetry operations ineven-TLs are: E, 2C3, 3C2′ (the three rotation axes are shown inFigure 1e and are lying in the σh plane), i (the inversion centeris shown as the pink solid circle in Figure 1d), 3σd (one of the

Figure 1. Symmetry operations in 1TL and 2TL MoS2/WSe2. (a) Sideview of 1TL. The axis of the two C3 operations (clockwise andanticlockwise) is denoted as the black line. The horizontal (σh) andvertical (σv) reflection operations are shown as the gray and yellowplanes, respectively. (b) Top view of 1TL. The axes of the three C2′operations are denoted as the green lines, which are lying in the σhplane. The top view of the σv planes are also demonstrated as thegreen lines. The gray diamond shows the unit cell from the top view.(c) Side view of the 1TL unit cell, where one Mo atom and two Satoms are contained. (d) Side view of 2TL with/AbA BaB/stacking.The axis of the C3 operations is denoted as the black line. Theinversion center is demonstrated by the pink solid circle. Thehorizontal (σh) and dihedral (σd) reflection operations are shown asthe gray and yellow planes, respectively. Note that σh is not one of theoperations in the space group for 2TL. (e) Top view of 2TL. Thepurple spheres represent the sites where two S atoms (top TL) sit ontop of one Mo atoms (bottom TL). The orange spheres represent thesites where one Mo atom (top TL) sits on top of two S atoms (bottomTL). The axes of the three C2′ operations are denoted as the greenlines, which are lying in the σh plane. The top view of the σd planes areshown as the yellow dashed lines. The gray diamond shows the unitcell. (f) Side view of the 2TL unit cell, which contains four S atomsand two Mo atoms. The two TLs are represented by two dashedboxes.

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dihedral reflection planes is represented as the yellow plane inFigure 1d, and the top views are shown as the yellow dashedlines in Figure 1e), 2S6 (clockwise and anticlockwise C6rotations followed by a σh reflection). Note that the σhreflection alone cannot be considered as a symmetry operationin even-TLs. Consequently, odd number TL crystals belong tothe symmorphic space group D3h

1 (P6 m2) which has noinversion symmetry, so that the irreducible representations ofthe zone center phonons can be written as: Γodd = ((3N − 1)/2)(A′1 + E″) + ((3N + 1)/2)(A″2 + E′), N = 1, 3, 5, ..., where Nis the number of TLs. While even number TL crystals belong tosymmorphic space group D3d

3 (P3m1) with inversion symmetry,the irreducible representations for the zone center phononsfollow: Γeven = (3N/2)(A1g + A2u + Eg + Eu), N = 2, 4, 6, etc.The normal mode displacements are shown in the SupportingInformation, Figure S-2 for 1TL, 2TL, and the bulk crystal.Let us consider the interlayer vibrations, where each TL is

displaced as a whole unit. In the bulk, there are two interlayeroptical phonon modes; that is, the Raman active E2g

2 (shearmode) and the optically inactive B2g

2 (breathing mode), wheretwo adjacent TLs vibrate out-of-phase in-plane and out-of-plane, respectively. In NTL systems, there are N−1 2-folddegenerate interlayer shear modes and N−1 interlayerbreathing modes. When N is odd, the interlayer breathingmodes are either Raman-active (A′1) or IR-active (A″2), whilethe interlayer shear modes are either Raman-active (E″) or bothRaman-active and IR-active (E′). When N is even, the interlayershear modes are either Raman-active (Eg) or IR-active (Eu) andthe interlayer breathing modes are also either Raman-active(A1g) or IR-active (A2u). The notations and Raman/IR activitiesof the phonon modes in 2H-MoS2/WSe2 are summarized inTable 1. The experimental observation of a given phonon mode

through Raman spectroscopy depends on the symmetryselection rules as well as the scattering geometry. The Ramanscattering intensity is proportional to |ei·R·es|

2, where ei is thepolarization vector of the incident light and es is that of thescattered light. R is the Raman tensor. A given phononmode can be observed by Raman scattering spectroscopy onlywhen |ei·R·es|

2 has a nonzero value. Raman tensors of theRaman-active interlayer vibrational modes can be predicted bygroup theory analysis as follows:

′⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟A

aa

b:

0 00 00 0

1

′ −⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟E

cc

dd:

0 00 00 0 0

,0 0

0 00 0 0

″−

−

⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟E

c

cd

d:

0 00 0 0

0 0,

0 0 00 00 0 (1)

for MoS2/WSe2 crystals with an odd number of TLs, and

⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟A

aa

b:

0 00 00 0

g1

−

⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟

⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟E

c dd c

dc

d c:

00

0 0 0,

0 00 0

0g

(2)

for even TLs.The experimental scattering geometries of our Raman

measurements can be represented by the Porto notations28

z (xx)z and z (xy)z, which correspond to parallel andperpendicular polarization configurations, respectively, in ourback-scattering geometry. Considering the Raman tensors of allof the Raman active modes, the polarization dependence of themodes can be predicted, as summarized in Table 1: theinterlayer breathing modes A′1 and A1g can only be observedunder the z(xx)z polarization configuration; the interlayer shearmodes E′ and Eg can be observed under both z(xx)z and z(xy)zpolarization configurations; while the other interlayer shearmode E″ cannot be observed under either configuration.Few-TL MoS2 and WSe2 crystals are prepared by mechanical

exfoliation,2 with the thickness determined by optical contrastand AFM measurements (see Figure 2b and SupportingInformation, Figure S-1). Figure 2c (left) shows typical anti-Stokes and Stokes Raman spectra of 1TL, 2TL, 4TL, and bulkMoS2 in the low frequency region (−55 to 55 cm−1) taken withthe z(xx)z polarization configuration. The spectra for the highfrequency E2g

1 and A1g modes (Figure 2c, right) exhibit ablueshift and redshift, respectively, from bulk to 1TL (in whichthese two modes actually have E′ and A′1 vibrationalsymmetries, respectively), in agreement with a previousreport.29 The Raman-active bulk mode E2g

2 (labeled as S1)corresponds to an interlayer shear mode where the adjacentTLs are vibrating out-of-phase by 180°. The S1 peak evolves tolower frequencies from bulk (∼32 cm−1) to 2TL (∼22 cm−1).Density functional theory (DFT) calculations indicate that theS1 peak corresponds in the NTL system to the highestfrequency shear mode. We also observe a broader peak in 2TLand 4TL (labeled as B1), which can be assigned to the lowestfrequency interlayer out-of-plane breathing mode by DFT. Thisassignment is consistent with the disappearance of B1 in thez(xy)z perpendicular polarization configuration (Figure 2d), inaccordance with the Raman selection rule, where the Ramanscattering intensity of a phonon mode is strictly determined byits Raman tensor and the polarization configuration ofthe experimental setup. Group theory predicts that, under thez(xy)z configuration, the Raman scattering intensity is zero forall of the breathing modes and nonzero for some shear modes;while under the z(xx)z configuration, both breathing and shearmodes could have nonzero Raman scattering intensities.Consequently, the out-of-plane A1g mode disappears in the

Table 1. Interlayer Vibrational Modes in Bulk and Few-TLMoS2/WSe2

a

interlayer shear modesinterlayer breathing

modes

bulk E2g2 (R) B2g

2 (inactive)NTL (N odd) E′ (I+R) E″ (R) A′1 (R) A″2 (I)NTL (N even) Eg (R) Eu (I) A1g (R) A2u (I)

aThe notation and Raman/IR activity of the phonon normal modesare listed here. The E′, Eg and E2g

2 phonon modes can be observedunder both the z(xx)z and z(xy)z polarization configurations, whilethe A′1 and A1g modes can only be observed under the z(xx)zpolarization configuration. The rest of the phonon modes cannot beobserved in our Raman measurements.

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z(xy)z configuration, while the in-plane E2g1 and E2g

2 shearmodes remain because of their nonzero off-diagonal matrixelements in the Raman tensors.30 It is important to note thatboth the B1 and S1 peaks are absent for samples with 1TL,which further confirms them as interlayer vibrational modes.Figure 1e, f shows similar Raman spectra for WSe2, with all theRaman peaks red-shifted with respect to those of MoS2,consistent with the larger mass per unit area in WSe2.Moreover, we observed another weak peak, labeled B2, around35 cm−1 in 4TL WSe2 under the z(xx)z configuration. DFTcalculations indicate that B2 corresponds to the breathing modewith the third lowest frequency, thus explaining why it wasobserved only for samples thicker than 3 TLs (recall that eachNTL has N−1 breathing modes).We next conduct a systematic thickness-dependent Raman

study on both materials. For the MoS2 sample, as the thicknessdecreases from bulk to 2TL, the S1 peak redshifts from ∼32cm−1 to ∼22 cm−1, as guided by the red dashed line (Figure 3a,b). In contrast, the second strongest peak B1 blueshifts from9TL (∼10 cm−1) to 2TL (∼40 cm−1) and crosses the S1 peakat 3TL. The high frequency modes E2g

1 and A1g are alsodispersed as a function of TL number, scaling with a blueshiftof ∼3 cm−1 and a redshift of ∼3.5 cm−1, respectively, from bulkto 1TL samples. The frequency dispersions of E2g

1 and A1g havebeen proposed to determine the thickness of few-TL MoS2,

29

which, however, are much less sensitive than using the S1 andB1 frequencies. The B1 peak is not observed in 10TL andabove, because of an inadequate signal-to-noise ratio. Two weakpeaks, labeled S2 and B2, can also be identified for samples witha thickness larger than 3 TLs, showing similar trends versusthickness with S1 and B1 (shown clearly in the SupportingInformation, Figure S-4, spectra before normalization). In WSe2we observe the same Raman-active modes with similar trends ofevolution versus thickness (Figure 3c, d). The pronounced

difference is that the B2 peak is much stronger in WSe2 (Figure3c). In both materials, the B1 and B2 modes are stronglysuppressed in the z(xy)z configuration, in agreement withRaman selection rules for breathing modes, as discussed above.The Raman spectra of these layered systems are computed

from density functional perturbation theory as implemented inthe Quantum-Espresso,3 within the local density approximation(LDA). Highly accurate convergence thresholds are required(see Methods and Supporting Information). Our calculationsindicate, as expected, that all low frequency modes (<55 cm−1)correspond to interlayer vibrations in which each TL moves asa single unit. Furthermore, the low-frequency phonon modesare essentially the same in both MoS2 and WSe2, except that thefrequencies are lower for WSe2. Figure 4a shows the twointerlayer modes in the bulk material, that is, the Raman activeshear mode E2g

2 and the optically inactive breathing mode B2g2 .

For the NTL systems, we obtain N−1 2-fold degenerateinterlayer shear modes and N−1 interlayer breathing modes, asexpected. We find that the observed S1 and S2 modes areinterlayer shear modes with the highest and third highestfrequencies for each NTL system, while the B1 and B2 modesare interlayer breathing modes with the lowest and third lowestfrequencies. This explains why S1 and B1 are observed in NTLswith N ≥ 2, while S2 and B2 are only observed for N ≥ 4. Wenote that the breathing modes with the second lowestfrequencies are missing because they are Raman-inactive,belonging to the symmetry groups A″2 for odd N and A2u foreven N (see Table 1). Shear modes with the second highestfrequencies belong to the symmetry groups E″ for odd N andEu for even N and, thus, cannot be observed in our Ramanmeasurements (see Table 1). Our DFT calculations furtherpredict that there are, in fact, other shear and breathing modes(Figure S6−S7 in the Supporting Information) that have thecorrect symmetry for observation; however, the calculated

Figure 2. Raman spectra of few-trilayer and bulk MoS2 and WSe2. (a) Crystal structure of 2H-MoS2/WSe2. The primitive unit cell runs over twotrilayers (TLs). (b) Optical images of 1−4TL MoS2 on 90 nm SiO2/Si substrates. The scale bar is 5 μm. (c−d) Stokes and anti-Stokes Ramanspectra of 1TL, 2TL, 4TL, and bulk MoS2 taken under the (c) z(xx)z polarized backscattering configuration and (d) z(xy)z polarizationconfiguration. (e−f) Stokes and anti-Stokes Raman spectra of 1TL, 2TL, 4TL, and bulk WSe2 under (e) z(xx)z configuration and (f) z(xy)zconfiguration. For increased clarity, all of the spectra in the low-frequency region are normalized by the intensity of the S1 peak, and the spectra inthe high frequency region are normalized by the intensity of the E2g

1 peak. The experimental scattering geometries of our Raman measurements arerepresented by the Porto notations28 z(xx)z and z(xy)z, where z and z indicate wave vectors of the incident laser beam and the collected scatteredlight, respectively. The two alphabets in parentheses represent the polarizations of incident and scattered light, respectively. We note that the highfrequency spectra will be discussed in further detail in future manuscripts.

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nonresonant Raman intensities, obtained within the Plazcekapproximation,31,32 are essentially zero, consistent with theexperimental findings. In all cases, the computed LDAfrequency behavior matches very well with the experiment(Figure 5a, b), with discrepancies of ∼4, ∼1.5, and ∼2 cm−1 forthe S1, B1, and B2 modes, respectively, for MoS2 and evenbetter agreement for WSe2. Since LDA does not treat vdWinteractions, we also compute the phonon frequencies using thevdW-DF functional,33,34 with Cooper’s exchange interactionterm.35 Interestingly, we find that, although LDA under-estimates the interlayer distance in comparison with the vdW-DF functional, the vdW-DF calculation overestimates thephonon frequencies compared with experiment (see Support-ing Information, Table S-2 and Figure S-8). Similar goodagreement with experiment was obtained for LDA calculationson the shear mode in multilayer graphene, suggesting that,although vdW-DF gives a more accurate description of theforces, LDA better describes the derivative of the forces withrespect to displacements.In Figure 4b, we schematically display the normal vibrational

displacements of the S1 and B1 modes in the NTL crystals (2 ≤N ≤ 9). In the S1 mode, adjacent TLs are distinctly out-of-phase, while in the B1 mode, the TLs can be divided into twogroups, with TLs in each group being approximately in-phasewith one another. This picture is consistent with the fact that

S1 is the highest frequency shear mode while B1 is the lowestfrequency breathing mode, because the frequency of aninterlayer phonon mode is larger if the adjacent TLs havemore out-of-phase displacement. Furthermore, in the case ofS1, a larger N implies more out-of-phase displacement betweenadjacent layers, leading to higher frequencies. In the case of B1,a larger N implies a greater proportion of approximately in-phase displacement, leading to lower frequencies. Similararguments can be made for S2 and B2 (Figure 4c). Comparingthe S1 mode with the bulk E2g

2 mode, it is clear that the S1mode evolves to the Raman-active E2g

2 mode in the bulk,although the vibration amplitudes of the surface layers areslightly smaller than for layers in the middle of the few-layermaterials. The reason for this difference is that the TLs at thesurface have only one nearest neighbor TL, in contrast to TLs inthe bulk that have two nearest neighbor layers. The excellentagreement between calculated and measured frequenciessuggest that the TLs are weakly coupled to the siliconsubstrate, which is consistent with measurements obtained forsuspended samples (see section V in Supporting Information)and a recent report on frictional properties.15

To quantify the aforementioned arguments, we consider asimple linear chain model (Figure 5c) for the interlayer modes,with each TL moving as one unit. The model further assumesthat only interactions between the nearest-neighbor layers are

Figure 3. Low-frequency Raman spectrum evolutions as a function of trilayer number in MoS2 and WSe2. (a−b) Low-frequency Raman spectra of1−12TL MoS2 measured using (a) the z(xx)z polarization configuration, and (b) the z(xy)z polarization configuration. (c−d) Low-frequencyRaman spectra of 1−7TL WSe2 measured under the (c) z(xx)z polarization configuration and (d) z(xy)z polarization configuration. The blue dotsare experimental data points, while the black solid curves are Lorentzian fittings to the data. The Rayleigh scattering background has been subtractedfor all of the spectra using a polynomial baseline treatment (see Supporting Information, Figure S-3). For increased clarity, all of the spectra arenormalized by the intensity of the strongest peak (corresponding to E2g

2 in the bulk and labeled as S1).

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important, and the substrate effects are neglected. The forceconstant K is the out-of-plane constant per unit area, Kz, for thebreathing modes, and the in-plane (shear) force constant perunit area, Kx, for the shear modes. A similar model haspreviously been used to explain the observed breathing mode inepitaxial thin films36 and shear modes in multilayer graphene.23

Solving this model, we obtain the eigenmodes

α π∝

− −α ⎡⎣⎢

⎤⎦⎥u

jN

cos( 1)(2 1)

2j

and the corresponding phonon frequencies (in cm−1)

ωμπ

α π= − −α

⎛⎝⎜

⎛⎝⎜

⎞⎠⎟⎞⎠⎟

Kc N2

1 cos( 1)

2 2

where j denotes the layer number and α = 1, 2, ..., N. The α = 1mode corresponds to the acoustic mode and α = 2, ..., Ncorrespond to the breathing modes (K = Kz) or shear modes(K = Kx), μ is the mass per unit area of the TMDs, and c is the

speed of light in cm/s. The eigenvector u is in the z directionfor the breathing mode and the x direction for the shear mode.The aforementioned expressions fit both the measured andcomputed frequencies perfectly (Figure 5a, b; α = N, N−2, 2, 4for S1, S2, B1, and B2, respectively), and the resulting forceconstants are shown in Table 2. Kz values derived from fits toexperimental data are almost the same in both materials (8.6 ×1019 N m−3), while the in-plane (shear) force constant Kx inWSe2 is 13% larger than in MoS2 (3.1 × 1019 N m−3 versus 2.7× 1019 N m−3); both are about 3 times smaller than Kz andmuch larger than that reported in few-layer graphene (1.28 ×1019 N m−3).23 We can also derive the corresponding elasticconstants, C33 and C44, C33 = Kzt and C44 = Kxt,

37 t being theequilibrium distance between the center of each TL. This givesexperimental values of C33 = 52.0 GPa and C44 = 16.4 GPa forMoS2, and C33 = 52.1 GPa and C44 = 18.6 GPa for WSe2.We note that the good fits imply not only that interlayer

interactions are dominated by interactions between nearest-neighbor layers, but also that the force constants Kx and Kz do

Figure 4. Vibrational normal modes of the interlayer shear and breathing modes in MoS2/WSe2. (a) The vibrational normal modes of the interlayershear (E2g

2 ) and breathing modes (B2g2 ) in bulk 2H-MoS2/WSe2. The shear mode is Raman-active, and the breathing mode is optically inactive. (b)

Vibrational normal modes of the highest frequency shear mode S1 (top) and the lowest frequency breathing mode B1 (bottom) from 2TL to 9TL.(c) Vibrational normal modes of the minor shear mode S2 (top) and the minor breathing mode B2 (bottom) from 4TL to 9TL. The arrows indicatethe direction of motion of the whole TL, and the length of the arrows represents the magnitude. The denoted frequencies are results of the firstprinciples calculations for both MoS2 (in purple) and WSe2 (in black).

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not change significantly as N is increased from 2 to 9 in NTLs;this is consistent with fits obtained for all computed interlayermode frequencies with the different N (see SupportingInformation, Figures S-9 and S-10), using a single K parameter.Remarkably, we note that in the limit, as N → ∞, the linearchain model with the above Kx values predicts S1 (E2g

2 )frequencies in very good agreement with the actual calculated/measured E2g

2 frequencies (Table 2), indicating that Kx isessentially unchanged from 2TLs to the bulk material. In arecent report, AFM measurements15 indicated that frictionincreased monotonically with decreasing number of layers inMoS2, and this was attributed to increased elastic compliance ofthinner films. We note that our results are not contradictory to,and in fact complement, these findings. As discussed by theauthors,15 there was relatively little interlayer sliding in theAFM measurements (indeed, the displacement in both in-planeand out-of-plane directions would be negligible under a ∼10nN lateral frictional force or normal load assuming the typicalAFM tip radius of 5 nm, using the force constants weextracted). Therefore the frictional characteristics probed bythe AFM experiments correspond to the limit where tip-layerinteractions are much weaker than interlayer interactions.However, the well-known lubricating properties of layeredTMDs are in fact related to the weak interlayer interactions, andhere, we show that these important interlayer interactions areessentially unchanged from 2 TLs to the bulk.

In conclusion, we have uncovered the Raman signature ofboth interlayer shear and breathing modes in 2H-MoS2/WSe2few-TL crystals. Two breathing modes are reported for the firsttime, where their appearance critically depends on thepolarization used in the Raman experiment. Such organ pipebreathing modes are expected to exist in many other 2Dcrystals. The shear and breathing modes provide effectiveprobes of the interlayer interactions that have importantimplications for both mechanical and electrical properties.

Methods. Sample Preparation. Single- and few-TL MoS2and WSe2 films were isolated from bulk crystals by Scotch tape-based mechanical exfoliation2 and were then deposited ontofreshly cleaned Si substrates with a 90 nm thick SiO2. The layernumbers can be determined by optical contrast and thicknessmeasurements using atomic force microscopy (Dimension3100 with a Nanoscope IIIa controller, Veeco, CA, USA)operated in a tapping mode under ambient conditions. Moredetails regarding sample preparation and characterization canbe found in the Supporting Information.

Raman Spectroscopy. Raman scattering spectroscopymeasurements were carried out at room temperature using amicro-Raman spectrometer (Horiba-JY T64000) equipped witha liquid nitrogen cooled charge-coupled device. The measure-ments were conducted in a backscattering configuration excitedwith a solid state green laser (λ = 532 nm). We used a reflectingBragg grating (OptiCrate) followed by another ruled reflectinggrating to filter the laser side bands, and as such we can achieve∼5 cm−1 limit of detection using most solid state or gas laserlines. We find our signal-to-noise ratio is adequate which rulesout the necessity of using a single monochromator config-uration with three notch filters as recently reported.23 Thebackscattered signal was collected through a 100× objectiveand dispersed by a 1800 g/mm grating under a triplesubtractive mode with a spectra resolution of 1 cm−1. Thelaser power at the sample surface was less than 1.5 mW forMoS2 and 0.3 mW for WSe2. Control measurements wereconducted using very low excitation power levels of 0.03 mWfor both materials. No detectable difference of the peak positionand full width half-maximum (fwhm) intensity was observedbetween Raman spectra using high and low excitation power

Figure 5. Frequency evolutions of measured and computed interlayer shear and breathing modes and the linear chain model interpretation. (a−b)Plot of shear and breathing mode frequencies as a function of TL number in (a) MoS2 and (b) WSe2. The experimental data (solid dots) and first-principles calculation results (open squares) match very well. The discrepancies for the S1, B1, and B2 modes in MoS2 are around 4 cm−1, 1.5 cm−1,and 2 cm−1, respectively. All of the fitting results in a and b are shown as the red solid lines for experimental data and black solid lines for DFTresults. The equations for the fits are based on the linear chain model as described in the text. (c) Schematic of the linear chain model for NTL ofMoS2/WSe2. One blue sphere stands for a TL. The force constant is K between nearest neighbor TLs.

Table 2. Force Constants Per Unit Area Derived from Fits tothe Linear Chain Model and the Corresponding PredictedS1 Frequencies in the Bulk

DFT (LDA) experiment

MoS2 Kz (1019 N m−3) 9.26 8.62

Kx (1019 N m−3) 3.51 2.72

bulk S1 frequency (cm−1) 36.1a (35.7) 31.8a (31.7)WSe2 Kz (10

19 N m−3) 8.38 8.63Kx (10

19 N m−3) 3.41 3.07bulk S1 frequency (cm−1) 24.8a (24.6) 23.5a (24.0)

aValues predicted by the linear chain model. The values in parenthesesare explicitly calculated by DFT (left column) or experimentallymeasured (right column) for the bulk material.

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levels. Thus, the laser heating effect can be excluded in ourmeasurements.Calculation Details. First-principles calculations of vibra-

tional Raman spectra are performed within density-functionaltheory (DFT) as implemented in the plane-wave pseudopo-tential code QUANTUM-ESPRESSO.3 The local densityapproximation (LDA)38 to the exchange-correlation functionalis employed in the norm-conserving (NC)39 pseudopotentialthroughout the calculation. For the purpose of comparison, theLDA calculations with projector-augmented wave (PAW)40

potentials for the electron-ion interaction are performed to testthe pseudopotential methods. To get converged results, plane-wave kinetic energy cutoffs of 65 and 550 Ry are used for thewave functions and charge density, respectively. The slabs areseparated by 16 Å of vacuum to prevent interactions betweenslabs (this value has been tested for convergence of phononfrequencies). A Monkhorst-Pack k-point mesh of 17 × 17 × 5and 17 × 17 × 1 are used to sample the Brillouin Zones for thebulk and thin films systems, respectively. In the self-consistentcalculation, the convergence threshold for energy is set to 10−9

eV. All of the atomic coordinates and lattice constants areoptimized with the Broyden−Fletcher−Goldfarb−Shanno(BFGS) quasi-Newton algorithm. During the structureoptimization, the symmetry of D6h

4 (P63/mmc) is imposed onthe bulk, while the symmetry of D3h

1 (P6m2) and D3d3 (P3 m1) is

imposed on the odd number TLs and even number TLs,respectively. The structures are considered as relaxed when themaximum component of the Hellmann−Feynman force actingon each ion is less than 0.003 eV/Å.With the optimized structures and self-consistent wave

functions, the phonon spectra and Raman intensities arecalculated within density-functional perturbation theory(DFPT) as introduced by Lazzeri and Mauri.32 For theDFPT self-consistent iteration, we used a mixing factor of 0.2and a high convergence threshold of 10−18 eV. According to theexperimental measurement, the LO-TO splitting,41,42 whichresults from the long-range dipole−dipole interactionsassociated with long wavelength longitudinal phonons, areincluded in the calculation with the momentum vector qapproaching zero from the x direction in the dynamical matrix.We find that the LO-TO splitting does not affect thefrequencies of the low frequency Raman modes reported here.

■ ASSOCIATED CONTENT*S Supporting InformationSample preparation and characterization; vibrational normalmodes of 1TL, 2TL, and bulk MoS2/WSe2; Lorentzianlineshape analysis; demonstration of breathing mode B2 andshear mode S2 in few-TL MoS2; substrate effect; first-principlescalculated phonon modes; linear chain model. This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail address: hzhang@ntu.edu.sg, queksy@ihpc.a-star.edu.sg, and qihua@ntu.edu.sg.

Author ContributionsY.Z. and X.L. contributed to this work equally. Y.Z., J.Z. andQ.X. conceived the idea. H.L., J.W., and H.Z. prepared thesamples and conducted thickness measurements. Y.Z., J.Z., andQ.X. performed the Raman scattering experiments. X.L.,C.K.G., and S.Y.Q. performed the first principles calculations

and explained the measured and computed frequencies usingthe linear chain model. P.T.A. and M.S.D. conducted grouptheory analysis. All authors analyzed data and cowrote themanuscript.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSQ.X. gratefully acknowledges the strong support of this workfrom Singapore National Research Foundation through afellowship grant (NRF-RF2009-06). This work was alsosupported in part by Ministry of Education via two Tier 2grants (MOE2011-T2-2-051 and MOE2012-T2-2-086), start-up grant support (M58113004), and New Initiative Fund(M58110100) from Nanyang Technological University(NTU). S.Y.Q. gratefully acknowledges support from theInstitute of High Performance Computing IndependentInvestigatorship. P.T.A. and M.S.D. acknowledge ONR-MURI-N00014-09-1-1063. H.Z. thanks the support from theSingapore National Research Foundation under a CREATEprogramme: Nanomaterials for Energy and Water Manage-m e n t , a n d NTU und e r t h e S t a r t -U p G r a n t(M4080865.070.706022).

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